Exploiting Forwardness: Satisfiability and Query-Entailment in Forward Guarded Fragment

Abstract

We study the complexity of two standard reasoning problems for Forward Guarded Logic ($\mathcal {FGF}$), obtained as a restriction of the Guarded Fragment in which variables appear in atoms only in the order of their quantification. We show that $\mathcal {FGF}$ enjoys the higher-arity-forest-model property, which results in $\textsc {ExpTime}$-completeness of its (finite and unrestricted) knowledge-base satisfiability problem. Moreover, we show that $\mathcal {FGF}$ is well-suited for knowledge representation. By employing a generalisation of Lutz’s spoiler technique, we prove that the conjunctive query entailment problem for $\mathcal {FGF}$ remains in $\textsc {ExpTime}$.

We find that our results are quite unusual as $\mathcal {FGF}$ is, up to our knowledge, the first decidable fragment of First-Order Logic, extending standard description logics like $\mathcal {ALC}$, that offers unboundedly many variables and higher-arity relations while keeping its complexity surprisingly low.